This paper considers multiple imputation (MI) approaches for handling non-monotone missing longitudinal binary responses when estimating parameters of a marginal model using generalized estimating equations (GEE). GEE has been shown to yield consistent estimates of the regression parameters for a marginal model when data are missing completely at random (MCAR). However, when data are missing at random (MAR), the GEE estimates may not be consistent; the MI approaches proposed in this paper minimize bias under MAR. The first MI approach proposed is based on a multivariate normal distribution, but with the addition of pairwise products among the binary outcomes to the multivariate normal vector. Even though the multivariate normal does not impute 0 or 1 values for the missing binary responses, as discussed by Horton et al. (Am Stat 57:229-232, 2003), we suggest not rounding when filling in the missing binary data because it could increase bias. The second MI approach considered is the fully conditional specification (FCS) approach. In this approach, we specify a logistic regression model for each outcome given the outcomes at other time points and the covariates. Typically, one would only include main effects of the outcome at the other times as predictors in the FCS approach, but we explore if bias can be reduced by also including pairwise interactions of the outcomes at other time point in the FCS. In a study of asymptotic bias with non-monotone missing data, the proposed MI approaches are also compared to GEE without imputation. Finally, the proposed methods are illustrated using data from a longitudinal clinical trial comparing four psychosocial treatments from the National Institute on Drug Abuse Collaborative Cocaine Treatment Study, where patients' cocaine use is collected monthly for 6 months during treatment.

中文翻译：

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使用具有非单调缺失纵向二进制结果的 GEE 的多重插补

本文考虑了在使用广义估计方程 (GEE) 估计边际模型参数时处理非单调缺失纵向二元响应的多重插补 (MI) 方法。当数据完全随机丢失 (MCAR) 时，GEE 已被证明可以对边际模型的回归参数产生一致的估计。但是，当数据随机缺失 (MAR) 时，GEE 估计值可能不一致；本文中提出的 MI 方法可以最大限度地减少 MAR 下的偏差。提出的第一种 MI 方法基于多元正态分布，但将二元结果之间的成对乘积添加到多元正态向量中。正如 Horton 等人所讨论的，即使多元正态不会为缺失的二元响应估算 0 或 1 值。(Am Stat 57:229-232, 2003), 我们建议在填充缺失的二进制数据时不要四舍五入，因为它可能会增加偏差。考虑的第二种 MI 方法是完全条件规范 (FCS) 方法。在这种方法中，我们根据其他时间点的结果和协变量为每个结果指定逻辑回归模型。通常，在 FCS 方法中，只包括其他时间的结果的主要影响作为预测因子，但我们探索是否可以通过在 FCS 中的其他时间点也包括结果的成对相互作用来减少偏差。在非单调缺失数据的渐近偏差研究中，所提出的 MI 方法也与 GEE 进行了比较，无需插补。最后，